New experimental techniques give a far more detailed picture of the motion of cellular components than was previously available. In single-particle tracking, computer-enhanced video microscopy is used to measure 2D motion of labeled membrane proteins or lipids on the cell surface, and 3D motion of proteins, protein complexes, viruses, and various subcellular structures in the cytoplasm and nucleus. Typically the spatial resolution is tens of nanometers and the time resolution is tens of milliseconds. One of the major results of single-particle tracking is that a significant fraction of proteins and lipids in the plasma membrane undergo various types of non-Brownian motion, including anomalous subdiffusion, directed motion, and confined motion. Transitions are observed between modes of motion. 3D motion within the cell is similarly complex. This project uses Monte Carlo simulations and percolation theory to study heterogeneous motion in heterogeneous cellular environments, and the biological consequences of this motion. The work will analyze various examples of hindered diffusion, such as the effect of the screened electrostatic interaction of charged extracellular domains of membrane proteins, and a simple geometric model of the cytoskeleton. The effects of membrane heterogeneity on reaction kinetics will be studied, specifically the role of lipid rafts or other domains in cellular signal transduction. Simulations will be used to develop improved methods of analysis of 2D and 3D single-particle tracking data. Experimental data on anomalous subdiffusion of Cajal bodies in the nucleus will be analyzed and simulated. The work on Cajal bodies will be the first test of a model in which anomalous subdiffusion indicates that the diffusing particle is randomly searching for its biological target and is equilibrating with a hierarchy of binding sites that bind the particle more strongly the more closely they resemble the target site. PUBLIC HEALTH RELEVANCE: Communication among and within cells are essential to life, and many drugs act by modulating cell signaling. My work uses computer simulations to examine the physical basis for this communication, asking: How is the cell surface organized for signaling? How do proteins and protein complexes move and find their biological targets in the crowded environments of the cell surface and interior? [unreadable] [unreadable] [unreadable]